Weyl functions of Dirac systems and of their generalizations: integral representation, inverse problem, and discrete interpolation

TL;DR

This paper investigates Weyl functions of Dirac and generalized systems, providing explicit solutions to direct and inverse problems, integral representations, and interpolation results, advancing the mathematical understanding of these systems.

Contribution

It introduces explicit solutions for direct and inverse problems and develops integral and interpolation representations for Weyl functions of Dirac and related systems.

Findings

Explicit solutions for direct and inverse problems

Integral representation of Weyl functions

Interpolation results for Weyl functions

Abstract

Self-adjoint Dirac systems and subclasses of canonical systems, which generalize Dirac systems are studied. Explicit and global solutions of direct and inverse problems are obtained. A local Borg-Marchenko-type theorem, integral representation of the Weyl function, and results on interpolation of Weyl functions are also derived.